低渗透油藏的压裂水平井三线性流试井模型

Trilinear-Flow Well Test Model of Fractured Horizontal Well in Low Permeability Reservoir

针对低渗透存在启动压力梯度的特点,建立了压裂水平井的三线性不稳定渗流数学模型,得到其在Laplace空间的解析解;通过Stehfest数值反演和Duhamel原理,得到了考虑井筒储存和表皮效应影响的压裂水平井井底压力值,对影响因素进行了研究。结果表明,启动压力梯度存在时,压裂水平井井底压力及压力导数曲线呈上翘趋势,且启动压力梯度越大,曲线越高,上翘的时间也越早;人工裂缝导流能力主要影响裂缝和双线性流出现时间的早晚;当裂缝间距达到一定值时,裂缝径向流才会出现,且裂缝间距越大,裂缝径向流持续时间越长;储容比影响压力导数曲线"凹子"的宽度和深度,储容比越小,"凹子"越宽越深;窜流系数决定"凹子"的位置,窜流系数越小,"凹子"就越靠右;井筒储集系数主要影响曲线的早期续流段。

According to the characteristics of the threshold pressure gradient for low permeability reservoir,a mathematical model of tri-linear flow unsteady percolation for fractured horizontal well is established;then deduced from its analytical solution in Laplace space.Bottom hole pressure of fractured horizontal wells is got after considering wellbore storage and skin factor by Stehfest numerical inversion and Duhamel principle,finally discussing the influence factors of the bottom hole pressure of fractured horizontal wells.The study result showed that the threshold pressure gradient made the dimensionless pressure and its derivative curves go up in late time,the bigger the threshold pressure gradient,the higher the curve and the earlier the curve going up appears;the fractured conductivity mainly influence the appeared time of bilinear-flow;the fracture radial flow appears only when the fracture interspacing achieves some extent,and the larger the space is,the fracture radial flow lasts longer;storage capacity ratio ω influences the hollow's width and depth of the pressure derivative curve,the smaller the ω,the wider the deeper hollow;cross-flow coefficient λ decides the position of hollow,the smaller the λ,the more right-hand the hollow;wellbore storage coefficient CD mainly affects the early freewheeling segment of the curve.